It is well known that a baseball bat is used for striking a ball during the game of baseball. The bat may be used with a conventional hardball or with a larger ball that is known as a softball. For the purposes of this description, the terms bat, ball, and baseball are used in their generic sense, and the invention described below may be adapted for use in any sport where an elongated member such as a bat is swung for the purpose of striking an object such as a ball.
The action of striking a baseball with a bat changes the momentum of the ball. Much of the momentum of the bat is thus transferred to the ball.
The momentum of the swung bat is the product of the mass of the bat and its velocity. The velocity of the bat primarily depends upon how much force a batter applies to the bat during the swing. It is helpful to think of the force applied to the bat by the batter as a “swinging force.”
Aerodynamic drag is a force that resists the swinging force. The magnitude of the drag force depends in part upon how fast the bat is swung or, more precisely, upon the relative speed of the bat through the air. The drag force has two components. One component is known as “pressure drag” or “form drag.” Pressure drag is caused by the pressure difference between the front or leading end of an object and the rear or trailing end of the object as that object is moved through the air. The magnitude of the pressure drag depends primarily upon the size and shape of the object, as well as the velocity of the object. A blunt object, such as a cylinder, will incur more pressure drag than a streamlined object, such as an airfoil.
It is noteworthy here that the movement of fluid (air) relative to an object such as a bat can be considered in terms of streamlines. A streamline is an imaginary line that is tangent to the direction of flow of the air. Every air particle in a streamline will follow the same direction or path around an object.
The other drag component that combines with pressure drag is known as “frictional drag” or “viscous drag.” Essentially, viscous drag is present within the boundary layer of the air. The boundary layer is the thin layer of air adjacent to the surface of any object moving through air. At the surface of the object the air in contact with the surface moves with a velocity of zero relative to the surface. The upper edge of the boundary layer is where the air moves at the same velocity as the surrounding streamlines (that is, where the velocity of the air near the object is not dependent on viscous effects).
The magnitude of viscous drag is influenced in part by the state of the boundary layer. The boundary layer state may be laminar or turbulent. In a laminar boundary layer, all of the streamlines lie in approximately parallel layers and do not cross. The slowest air particles are in the streamlines or layers nearest the surface of the object, and the air particles in each higher layer move in streamlines that are faster than the one below. This pattern is termed a velocity gradient.
As a laminar boundary layer continues along a surface, the height of the boundary layer increases until it eventually undergoes a transformation to a turbulent boundary layer through a process known as transition. In a turbulent boundary layer, the flow is comprised of an average velocity gradient with many random temporal and spatial internal fluctuations. Generally, turbulent boundary layers are thicker and produce more viscous drag than laminar boundary layers.
The roughness of the surface of the object affects the state of the boundary layer (laminar or turbulent). Roughened surfaces will generally cause a laminar boundary layer to experience an earlier transition to a turbulent boundary layer.
Laminar air flow around an object will produce less viscous drag (as compared to turbulent flow), but such flow is also prone to a phenomenon called flow separation whereby the air traveling over a surface becomes detached from the surface, creating a low pressure region immediately downstream from where the flow separates from the object. Such low-pressure regions near the trailing side of an object add a significant amount of pressure drag. Turbulent-boundary-layer flow, as compared to laminar flow, is less likely to separate from an object. Accordingly, in some instances where laminar boundary layer separation is likely to occur (as with a blunt object), it is desirable to reduce flow separation by (i) contouring or streamlining the shape of the object and/or (ii) by intentionally roughening the surface of the object, thereby to induce turbulent-boundary-layer flow and eliminate or reduce pressure drag that might otherwise be produced by flow separation.